| G.E. Martin - Mathematics - 1997 - 536 pages
...the vertical angles equal to one another. (Theorem 14.11) 16. In any triangle, if one of the sides **be produced, the exterior angle is greater than either of the interior** and opposite angles. (Theorem 17.9) 17. In any triangle two angles taken together in any manner are... | |
| Daniel Pedoe - Mathematics - 1988 - 468 pages
...another, they make the vertical angles equal to one another. 16 In any triangle, if one of the sides **be produced, the exterior angle is greater than either of the interior** and opposite angles. 17 In any triangle two angles taken together in any manner are less than two right... | |
| Saul Stahl - Geometry, Non-Euclidean - 1993 - 320 pages
...students' memory, Euclid's proof is summarized below. Proposition 16. In any triangle, if one of the sides **be produced, the exterior angle is greater than either of the interior** and opposite angles. PROOF: Let ABC be a triangle, and let one side of it BC be produced to D (Fig.... | |
| Law - 1903 - 960 pages
...numbers is 13, the difference of their squares is 39. Find the numbers. SECOND PAPEK. EUCLID. 2. I f any **side of a triangle be produced, the exterior angle is greater than either of the interior** non-adjacent angles. 1. Prove that, it at a point in a right liiic, two other right lines on opposite... | |
| Troels Kardel - Medical - 1994 - 270 pages
...respectively, namely those which the equal sides subtend. I. 16. In any triangle, if one of the sides **be produced, the exterior angle is greater than either of the interior** and opposite angles. I. 18. In any triangle the greater side subtends the greater angle. I. 20. In... | |
| James Clerk Maxwell - Science - 1990 - 836 pages
...and annotations on the flyleaf by Maxwell, is in Maxwell's library (Cavendish Laboratory, Cambridge). **(Theorem) ' If one side of a triangle be produced,...exterior angle is greater than either of the interior,** and opposite angles' (Elements: 20). the angle ADB (Prop. 5). Upon AB describe a segment of a circle... | |
| F. Jamil Ragep, Sally P. Ragep, Steven John Livesey - Science - 1996 - 634 pages
...the three propositions quoted by Thabit b. Qurra. Theorem I,16: In any triangle, if one of the sides **be produced, the exterior angle is greater than either of the interior** and opposite angles.35 Table I 36 35 Heath [1956], vol. l,p. 279. 36 Since Thabit omitted here the... | |
| Howard Whitley Eves - Mathematics - 1997 - 370 pages
...line. Let us briefly consider, for example, Proposition I 16: In any triangle, if one of the sides **be produced, the exterior angle is greater than either of the interior** and opposite angles. A precis of Euclid's proof runs as follows. Let ABC (Figure 2.2) be the given... | |
| Judith Cederberg - Mathematics - 2004 - 472 pages
...another, they make the vertical angles equal to one another. 16. In any triangle if one of the sides **be produced, the exterior angle is greater than either of the interior** and opposite angles. 17. In any triangle two angles taken together in any manner are less than two... | |
| Mathematical Association of America - Mathematics - 2003 - 572 pages
...they make the vertical angles equal to one another. Prop. 16: In any triangle, if one of the sides **be produced, the exterior angle is greater than either of the interior** and opposite angles. Prop. 19: In any triangle the greater angle is subtended by the greater side.... | |
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